#Numerical Analysis

In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function f, its derivative f′, and an initial guess x₀ for a root of f. If f satisfies certain assumptions and the initial guess is close, then x₁ = x₀ - f(x₀)/f'(x₀) is a better approximation of the root than x₀. Geometrically, (x₁, 0) is the x-intercept of the tangent of the graph of f at (x₀, f(x₀)): that is, the improved guess, x1, is the unique root of the linear approximation of f at the initial guess, x₀. The process is repeated as xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended to complex functions and to systems of equations. Follow @mathvibes01 for more 🔥 #math #manim #python #mathematics

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Carl Friedrich Gauss, often referred to as the „Prince of Mathematicians,“ was a German mathematician who laid the foundations of many modern mathematical disciplines with his contributions to number theory, algebra, analysis, and geometry. Even as a child, he showed an extraordinary talent that made him one of the most influential thinkers of his time. Gauss worked on topics as diverse as measuring the Earth, developing statistical methods, and studying magnetic fields. His precise working methods and ability to connect seemingly unrelated mathematical concepts made him a legend. His ideas and methods continue to shape mathematics today and inspire generations of researchers. Explore math with us. Maths is easy #maths #physics #physics #engineering #mathematics #calculus #math

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Srinivasa Ramanujan was indeed a brilliant mathematician, often regarded as one of the greatest mathematical minds in history. Born on December 22, 1887, in Erode, Tamil Nadu, India, Ramanujan made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite lacking formal training in mathematics, Ramanujan independently developed many theorems and results that were later proven by other mathematicians. He sent his work to renowned mathematicians in Europe, including G.H. Hardy, who recognized his talent and invited him to Cambridge University. Ramanujan's collaboration with Hardy resulted in groundbreaking research. Some of Ramanujan's notable contributions include his work on modular forms, mock theta functions, partitions, and his famous formulae for pi. His discoveries have applications in various areas of mathematics and have influenced fields such as quantum physics. Unfortunately, Ramanujan's life was cut short; he passed away on April 26, 1920, at the age of 32. His legacy lives on, and he continues to be an inspiration for mathematicians worldwide. The story of his life and work is a testament to the power of pure intuition and natural mathematical ability. #srinivasaramanujan #indianmathematics #geniusmathematician #vedprep #srinivasaramanujanequations #srinivasaramanujanbirthday #mathsacademy #indianmathematicianday

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